# Applicability of new CTOD calculation formula to various a0/W conditions and BxB configuration

### Significance Statement

A new CTOD calculation method considering the variation of crack tip blunting due to strain hardening has recently been developed. New calculation formula was proposed that was applicable to standard crack depth to width ratio conditions, a0/W=0.45-0.55 based on a number of 3-dimensional finite element outcomes, which were efficient in the parametric study for the establishment of a computational formula for crack tip opening displacement. The modification from the current formula would be the introduction of a coefficient ‘f’. This describes the blunting configuration established by the strain-hardening exponent.

In their recent report, the authors clarified deformation behavior for a wide range of crack depth to width ratio conditions. They obtained a number of important pieces, namely, clear rotational deformation in the ligament observed under all conditions, coordination of the rotational center as a function of crack depth to width ratio only, and the plastic exponent of the crack tip opening displacement computed by the plastic hinge relationship between plastic component of crack mouth opening displacement and rotational factor.

In the current study, Tomoya Kawabata and co-workers at The University of Tokyo modified and developed the calculation formula based on that knowledge to enable the application to an extended range of crack depth to width ratio conditions. They also investigated the possibility of simple application of the suggested formula to the BxB type specimen. They validated the finite element analysis for both Bx2B and BxB type specimen by silicone rubber replica approach. Their work is published in Engineering Fracture Mechanics.

A previous study analyzing the plastic deformation behavior over a wide range of crack depth to width ratio conditions indicated that there was a slight deviation from complete formation of a plastic hinge model in the computation of plastic component of crack tip opening displacement even when the blunting behavior was corrected implementing the strain hardening exponent. Under normal conditions i.e. a0/W =0.5, correction was not needed. The amount of deviation of a0/W of 0.3-0.7 could be linearly arranged with a0/W.

However, in the shallower zone of 0.1, the deviation was larger than the linear extrapolation from the other crack depth to width ratio conditions. This could be related to the unique characteristics observed under shallower conditions than 0.2. When a correction coefficient for this deviation was introduced in the formula covering various crack depth to width ratio conditions, the authors supposed that the coefficient could be separated into two terms.

This report reveals that the plastic hinge model can be implemented to crack depth to width ratio conditions other than the 0.45-0.55 range dictated by an observation of plastic deformation for wider crack depth to width ratio conditions. Coordination of the rotational center was steady irrespective of the load level and strain-hardening exponent.

Based on the knowledge of the plastic deformation behavior analyzed in the previous report, the authors were able to come up with a new crack tip opening displacement calculation formula covering a range of crack depth to width ratio conditions. They introduced a new coefficient optimized by B=25mm, Bx2B and several crack depth to width ratio conditions into the formula. This new formula has high accuracy with wide range of  thickness and with the BxB type specimen without modification of the formula.

### About the author

Shuji AIHARA was born in 1953. He received his doctor’s degree in 1981 from the University of Tokyo. He is a full professor and works at the University of Tokyo. Also he is currently managing Japan Welding Engineering Society as the President.

His interests includes fracture mechanics and materials science, especially prediction of toughness of weld heat-affected zone of high-strength steels and dynamic crack propagation in high-pressure pipelines and ship hull structures.

### About the author

Yukito Hagihara received his Doctor of Engineering from the University of Tokyo, Japan, in 1973.Then, he has worked at Nippon Steel Corporation for 28 years and has engaged in the research field fracture mechanics, fracture toughness of steels and fitness for service assessment of welded structures, such as ships, offshore structures, LNG storage tanks, bridges and so on. From 2001, he has worked at National Institute for Materials Science for 3 years.

His main task was research on evaluating ultra-fine grained steel as a part of national research project of super-metal. In 2004, he moved to Sophia University, and has worked as a Professor at Department of Mechanical Engineering, Faculty of Science and Technology, until 2012. He has engaged in research on hydrogen embrittlement and delayed fracture characteristics of high strength steels, and proposed a CSRT (conventional strain rate test) technique for delayed fracture evaluation.

### About the author

Tomoya KAWABATA was born in Osaka, Japan. He graduated from Kyoto University in 1994 and worked in Nippon Steel and Sumitomo Metal Corporation for over 20 years. He has received his ”Doctor of Engineering” from Osaka University in 2006. He worked in The University of Tokyo from 2014 as an Associate Professor.

His interests is the effects of microstructural factors on fracture safety issues of large welded structures whose failure modes are brittle fracture, ductile crack extension and fatigue. He is an author of over 60 publications in engineering mechanics field and an inventor of over 100 patents.

### About the author

Yoichi Kayamori has been working with Nippon Steel & Sumitomo Metal Corporation since 1994, and a senior researcher in the field of fracture safety technology. He conducted his PhD research under the supervision of Professor R. Smith at Imperial College London from 2002 to 2004, and was awarded PhD from the University of London and DIC from Imperial College London. His research interests are in the wide area of fracture such as brittle/ductile fracture, fatigue, corrosion fatigue and stress corrosion cracking in steel.

He has been a member of the CTOD Toughness Evaluation Committee of the Japan Welding Engineering Society and Head of the Mechanics Group in the Editorial Committee of the Japan Welding Society.

### About the author

Fumiyoshi Minami was born in Osaka in 1954. He has obtained ”Doctor of Engineering” in the field of welding mechanics from Osaka University in 1985. He is a full professor and has been working in the Division of Materials and Manufacturing Science, Graduate School of Engineering in Osaka University. In 2014 he moved to Joining and Welding Research Institute (JWRI), Osaka University. He is currently managing JWRI as the Director.

His interests include the fracture mechanics and structural integrity assessment of steel components. He is an author of more than 160 publications in scientific journals, such as Engineering Fracture Mechanics, International Journal of Fracture, etc.

He is the President of Japan Welding Society and a member of IIW Board of Director.

### About the author

Mitsuru Ohata, Has a PhD from Osaka University in 1997. Currently serve as a full professor at Osaka University (Japan), Graduate School of Engineering, Department of Materials and Manufacturing Science.

### About the author

Tetsuya TAGAWA has received doctor degree in 1994 from Nagoya University (Japan), and worked in Nagoya University. He has contributed as a university faculty to research and education about fatigue and fracture mechanisms in metallic materials for 26 years. Then, he joined to JFE Steel Corporation, and now continues his research in Steel Research Laboratory. His interests are wide from phenomenological approach in fatigue and fracture behaviors to practical standardizations of evaluation procedures. He is an author of about 90 publications in engineering journals.

### About the author

Yoichi Yamashita is the senior researcher at IHI Corporation and he has 22-years-experience as a researcher and an engineer at IHI Corporation. He received the M.S. degree, in 1995 and the B.S. degree, in 1993 from the University of Tokyo. He received his Ph.D in engineering at Osaka University in 2008.

### Reference

Tomoya Kawabata, Tetsuya Tagawa, Yoichi Kayamori, Mitsuru Ohata, Yoichi Yamashita, Masao Kinefuchi, Hitoshi Yoshinari, Shuji Aihara, Fumiyoshi Minami, Hiroshi Mimura, Yukito Hagihara. Applicability of new CTOD calculation formula to various a0/W conditions and BxB configuration. Engineering Fracture Mechanics, volume 179 (2017), pages 375–390.